In the large-Hilbert-space limit, Floquet chaotic dynamics with Haar random gates produce linear shot-noise scaling of quantum Fisher information, with super-linear advantages at finite sizes, while local random circuits asymptotically mimic global unitaries.
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Conjecture that the Hausdorff dimension of the frontier of the SFF random walk approaches 4/3 for chaotic Hamiltonians and 1 for integrable ones, with proofs of Gaussian statistics under Lyapunov conditions on degeneracies and exact moments for unequal-step walks.
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Asymptotic Metrological Scaling and Concentration in Chaotic Floquet Dynamics
In the large-Hilbert-space limit, Floquet chaotic dynamics with Haar random gates produce linear shot-noise scaling of quantum Fisher information, with super-linear advantages at finite sizes, while local random circuits asymptotically mimic global unitaries.
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Integrability and Chaos via fractal analysis of Spectral Form Factors: Gaussian approximations and exact results
Conjecture that the Hausdorff dimension of the frontier of the SFF random walk approaches 4/3 for chaotic Hamiltonians and 1 for integrable ones, with proofs of Gaussian statistics under Lyapunov conditions on degeneracies and exact moments for unequal-step walks.